Mathematics

# Control theory and opitimization I by M.I. Zelikin, S.A. Vakhrameev

By M.I. Zelikin, S.A. Vakhrameev

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Extra resources for Control theory and opitimization I

Example text

3-6. When the mill charge is large, ki is inversely proportional to f with approximately hyperbolic character. At decreasing charges, when the mill charge fills approximately the interstitial volume of the static ball charge, the effectiveness of grinding declines, because collisions are mainly between the balls, on the one hand, and the specific value of the energy exceeds that necessary to cause agglomeration, on the other. ) Considering the above behaviours, the breakage rates ki can be given by the following complex formula [154] (in good agreement with experience): kj d f = -~ I l.

Using f(t) = t J o [x(t)-m(t)] dt (5,1,4) 53 MATERIAL FLOW MODELS OF CLOSED CIRCUIT GRINDING N sit) viti mit) g(t) Fig. 1-5 General material flow model of the mill- classifier joint system 1'010 Go x Xo Fig. 1-6 Static characteristics of closed circuit grinding with respect to the total mill feed X 54 CHAPTERS While in Fig. 1-4 f(t) means the material in the whole grinding system, in this case f(t) is related to the material in the mill. 4) gives also this in steady-state. 1). This model describes well, even down to detail, the quantitative behaviour of the mill and, disregarding the delays, it can be considered equivalent to Fig.

3-6 23 kj Dependence of the breakage rate on the material f being in the mill the load of material f in the mill (or filling factor), see Fig. 3-6. When the mill charge is large, ki is inversely proportional to f with approximately hyperbolic character. At decreasing charges, when the mill charge fills approximately the interstitial volume of the static ball charge, the effectiveness of grinding declines, because collisions are mainly between the balls, on the one hand, and the specific value of the energy exceeds that necessary to cause agglomeration, on the other.